JEE Main 2022 (Online) 27th June Morning Shift

Five numbers \({x_1},{x_2},{x_3},{x_4},{x_5}\) are randomly selected from the numbers 1, 2, 3, ......., 18 and are arranged in the increasing order \(({x_1} < {x_2} < {x_3} < {x_4} < {x_5})\). The probability that \({x_2} = 7\) and $${x_4} ...

Let X be a random variable having binomial distribution B(7, p). If P(X = 3) = 5P(x = 4), then the sum of the mean and the variance of X is :

The lengths of the sides of a triangle are 10 + x2, 10 + x2 and 20 \(-\) 2x2. If for x = k, the area of the triangle is maximum, then 3k2 is equal to :

The number of distinct real roots of x4 \(-\) 4x + 1 = 0 is :

If the sum of all the roots of the equation \({e^{2x}} - 11{e^x} - 45{e^{ - x}} + {{81} \over 2} = 0\) is \({\log _e}p\), then p is equal to ____________.

\(x = \sum\limits_{n = 0}^\infty {{a^n},y = \sum\limits_{n = 0}^\infty {{b^n},z = \sum\limits_{n = 0}^\infty {{c^n}} } }\), where a, b, c are in A.P. and |a| < 1, |b| < 1, |c| < 1, abc \(\ne\) 0, then :

If the sum of the first ten terms of the series
\({1 \over 5} + {2 \over {65}} + {3 \over {325}} + {4 \over {1025}} + {5 \over {2501}} + \,\,....\)
is \({m \over n}\), where m and n are co-prime numbers, then m + n is equal to _____________...

In an isosceles triangle ABC, the vertex A is (6, 1) and the equation of the base BC is 2x + y = 4. Let the point B lie on the line x + 3y = 7. If (\(\alpha\), \(\beta\)) is the centroid of \(\Delta\)ABC, then 15(\(\alpha\) + \(\beta\)) is ...

The value of \(\cos \left( {{{2\pi } \over 7}} \right) + \cos \left( {{{4\pi } \over 7}} \right) + \cos \left( {{{6\pi } \over 7}} \right)\) is equal to :

Let \(\overrightarrow a = \widehat i + \widehat j - \widehat k\) and \(\overrightarrow c = 2\widehat i - 3\widehat j + 2\widehat k\). Then the number of vectors \(\overrightarrow b\) such that $$\overrightarrow b \times \overrightarrow ...

The current flowing through an ac circuit is given by
I = 5 sin(120\(\pi\)t)A
How long will the current take to reach the peak value starting from zero?

A 220 V, 50 Hz AC source is connected to a 25 V, 5 W lamp and an additional resistance R in series (as shown in figure) to run the lamp at its peak brightness, then the value of R (in ohm) will be _____________.

A hydrogen atom in its ground state absorbs 10.2 eV of energy. The angular momentum of electron of the hydrogen atom will increase by the value of :
(Given, Planck's constant = 6.6 \(\times\) 10\(-\)34 Js).

A beam of monochromatic light is used to excite the electron in Li+ + from the first orbit to the third orbit. The wavelength of monochromatic light is found to be x \(\times\) 10\(-\)10 m. The value of x is ___________.
[Given hc = 1242 eV...

A force of 10 N acts on a charged particle placed between two plates of a charged capacitor. If one plate of capacitor is removed, then the force acting on that particle will be.

A capacitor of capacitance 50 pF is charged by 100 V source. It is then connected to another uncharged identical capacitor. Electrostatic energy loss in the process is ___________ nJ.

Two blocks of masses 10 kg and 30 kg are placed on the same straight line with coordinates (0, 0) cm and (x, 0) cm respectively. The block of 10 kg is moved on the same line through a distance of 6 cm towards the other block. The distance t...

What percentage of kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary particle of 5 times its mass?
(Assume the collision to be head-on elastic collision)

A pendulum of length 2 m consists of a wooden bob of mass 50 g. A bullet of mass 75 g is fired towards the stationary bob with a speed v. The bullet emerges out of the bob with a speed \({v \over 3}\) and the bob just completes the vertical...

The height of a transmitting antenna at the top of a tower is 25 m and that of receiving antenna is, 49 m. The maximum distance between them, for satisfactory communication in LOS (Line-Of-Sight) is K\(\sqrt5\) \(\times\) 102 m. The value o...

A 72 \(\Omega\) galvanometer is shunted by a resistance of 8 \(\Omega\). The percentage of the total current which passes through the galvanometer is :

A cell, shunted by a 8 \(\Omega\) resistance, is balanced across a potentiometer wire of length 3 m. The balancing length is 2 m when the cell is shunted by 4 \(\Omega\) resistance. The value of internal resistance of the cell will be _____...

The current density in a cylindrical wire of radius 4 mm is 4 \(\times\) 106 Am\(-\)2. The current through the outer portion of the wire between radial distances \({R \over 2}\) and R is ____________ \(\pi\) A.

An \(\alpha\) particle and a carbon 12 atom has same kinetic energy K. The ratio of their de-Broglie wavelengths \(({\lambda _\alpha }:{\lambda _{C12}})\) is :

Match List-I with List-II :

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Identify the correct Logic Gate for the following output (Y) of two inputs A and B.

Consider a light ray travelling in air is incident into a medium of refractive index \(\sqrt{2n}\). The incident angle is twice that of refracting angle. Then, the angle of incidence will be :

Given below are two statements :
Statement I : The law of gravitation holds good for any pair of bodies in the universe.
Statement II : The weight of any person becomes zero when the person is at the centre of the earth.
In the light of the...

A mixture of hydrogen and oxygen has volume 2000 cm3, temperature 300 K, pressure 100 kPa and mass 0.76 g. The ratio of number of moles of hydrogen to number of moles of oxygen in the mixture will be:
[Take gas constant R = 8.3 JK\(-\)1mol$...

In a carnot engine, the temperature of reservoir is 527\(^\circ\)C and that of sink is 200 K. If the work done by the engine when it transfers heat from reservoir to sink is 12000 kJ, the quantity of heat absorbed by the engine from reservo...

A system of two blocks of masses m = 2 kg and M = 8 kg is placed on a smooth table as shown in figure. The coefficient of static friction between two blocks is 0.5. The maximum horizontal force F that can be applied to the block of mass M s...

The susceptibility of a paramagnetic material is 99. The permeability of the material in Wb/A-m, is :
[Permeability of free space \(\mu\)0 = 4\(\pi\) \(\times\) 10\(-\)7 Wb/A-m]

A projectile is launched at an angle '\(\alpha\)' with the horizontal with a velocity 20 ms\(-\)1. After 10 s, its inclination with horizontal is '\(\beta\)'. The value of tan\(\beta\) will be : (g = 10 ms\(-\)2).

A girl standing on road holds her umbrella at 45\(^\circ\) with the vertical to keep the rain away. If she starts running without umbrella with a speed of 15\(\sqrt2\) kmh\(-\)1, the rain drops hit her head vertically. The speed of rain dro...

The velocity of a small ball of mass 'm' and density d1, when dropped in a container filled with glycerin, becomes constant after some time. If the density of glycerin is d2, then the viscous force acting on the ball, will be :

The area of cross-section of a large tank is 0.5 m2. It has a narrow opening near the bottom having area of cross-section 1 cm2. A load of 25 kg is applied on the water at the top in the tank. Neglecting the speed of water in the tank, the...

The displacement of simple harmonic oscillator after 3 seconds starting from its mean position is equal to half of its amplitude. The time period of harmonic motion is :

A silver wire has a mass (0.6 \(\pm\) 0.006) g, radius (0.5 \(\pm\) 0.005) mm and length (4 \(\pm\) 0.04) cm. The maximum percentage error in the measurement of its density will be :

In Young's double slit experiment the two slits are 0.6 mm distance apart. Interference pattern is observed on a screen at a distance 80 cm from the slits. The first dark fringe is observed on the screen directly opposite to one of the slit...

An observer moves towards a stationary source of sound with a velocity equal to one-fifth of the velocity of sound. The percentage change in the frequency will be :